1) Field of the Invention
The present invention relates to a technology for calculating magnetic interaction of molecules, crystalline compounds, and high polymer compounds exhibiting ferromagnetism.
2) Description of the Related Art
Conventionally, a theory of magnetic characteristics has developed using a Heisenberg model which targets a localized electron system and a Stoner model which targets an itinerant electron system. However, since the Heisenberg model produces a rough approximation and cannot be easily handled, the Heisenberg model has been culled out in favor of the Stoner model.
The Stoner model has passed through a physical examination in a Hubbard model, an Anderson model, or the like which are phenomenological models and, at present, has settled to a band calculation method based on a density functional theory. In the recent band calculation method based on the density functional theory, an effective exchange interaction energy can be obtained with a calculation accuracy which is satisfactory to some extent (Sakuma Akimasa, Hitachi Metals Technical Journal, 16, 55 to 60 (2000)).
However, the conventional evaluation method (band calculation method) targets, for calculation, an itinerant electron system which uses a Bloch function as a base, and, therefore, it has been difficult to handle a localized electron system or an intermediate electron system between the itinerant electron system and the localized electron system.
The band calculation method can be easily applied to an extremely small crystal system such as iron or nickel crystals and oxides thereof. However, even though the band calculation method is applied to a small crystal system, an enormous quantity of calculation is required. Therefore, the following problem is left. That is, for example, it is substantially difficult to apply the band calculation method to an actual huge crystal system such as a neodymium-based rare earth magnetic material (Nd2Fe14B crystal) from the viewpoint of calculation quantity.
On the other hand, in consideration of the circumstances, a method of easily predicting ferromagnetism by changing molecular orbitals has been proposed (Japanese Patent Application Laid-Open No. H11-6825). However, magnetic characteristics detected in an experiment cannot be calculated using this method, and the calculation is limited to an organic high polymer compound. For this reason, the method poses a problem in a practical use.
It is an object of this invention to obtain a method of calculating a magnetic interaction in not only an itinerant electron system but also a localized electron system or an intermediate electron system across both the electron systems.
The magnetic interaction calculation method according to one aspect of this invention comprises calculating a magnetic interaction of molecules using a localized magnetic orbital xcex7a which satisfies a maximum overlap condition                                           ∑                                          xe2x80x83                            ⁢              a                                      xe2x80x83                                ⁢                      xe2x80x83                    ⁢                      "LeftBracketingBar"                          ⟨                                                η                  a                                |                                  ω                  a                                            ⟩                        "RightBracketingBar"                          =                  xe2x80x83                ⁢                  maximum          ⁢                      xe2x80x83                    ,                      xe2x80x83                    ⁢          wherein                                                  η          a                =                  xe2x80x83                ⁢                              ∑            i                          xe2x80x83                                ⁢                      xe2x80x83                    ⁢                                    T              ai                        ⁢                          φ              i                                          
and xcfx89a is a reference orbital given by             ω      a        =                  ∑        i                  xe2x80x83                    ⁢              xe2x80x83            ⁢                        c          ai                      -            1                          ⁢                  φ          i                      where            φ      i        =                  ∑        a            ⁢              xe2x80x83            ⁢                        c          ai                ⁢                  χ          a                    
is a molecular orbital expressed as a linear combination of an atomic orbital "khgr"a, cai is an expansion coefficient, caixe2x88x921 is an inverse matrix of the expansion coefficient cai, and Tai is the expansion coefficient of the a-th orbital xcex7a for the i-th molecular orbital xcfx86i.
The magnetic interaction calculation method according to another aspect of this invention comprises calculating a magnetic interaction of crystalline compounds or high polymer compounds using a localized magnetic crystal orbital xcex7a (k) which satisfies a maximum overlap condition                                           ∑            a                    ⁢                      xe2x80x83                    ⁢                      "LeftBracketingBar"                          ⟨                                                η                  a                                |                                  ω                  a                                            ⟩                        "RightBracketingBar"                          =                  xe2x80x83                ⁢                  maximum          ⁢                                    xe2x80x83                        ,                    ⁢                      xe2x80x83                    ⁢          wherein                                                              η            a                    ⁡                      (            k            )                          =                  xe2x80x83                ⁢                              ∑            i                    ⁢                      xe2x80x83                    ⁢                                                    T                ai                            ⁡                              (                k                )                                      ⁢                                          φ                i                            ⁡                              (                k                )                                                        
and xcfx89a (k) is a reference orbital given by                     ω        a            ⁡              (        k        )              =                  ∑        i            ⁢              xe2x80x83            ⁢                                                  c              ai                        ⁡                          (              k              )                                            -            1                          ⁢                              φ            i                    ⁡                      (            k            )                                where                    φ        i            ⁡              (        k        )              =                  ∑        a            ⁢              xe2x80x83            ⁢                                    c            ai                    ⁡                      (            k            )                          ⁢                              ∑            R                    ⁢                      xe2x80x83                    ⁢                                    exp              ⁡                              (                                  ⅈ                  ⁢                                      xe2x80x83                                    ⁢                  kR                                )                                      ⁢                                          χ                a                            ⁡                              (                R                )                                                        
is a crystal orbital expressed as a linear combination of an atomic orbital "khgr"a, cai (k) is an expansion coefficient, cai (k)xe2x88x921 is an inverse matrix of the expansion coefficient cai (k), Tai (k) is the expansion coefficient of the a-th localized magnetic orbital xcex7a (k) for the i-th crystal orbital xcfx86i (k), k is a wave vector ranging from xe2x88x92xcfx80/c to xcfx80/c where c is primitive vectors, and R is a vector representing crystal periods.
The magnetic characteristic value calculation method according to still another aspect of this invention comprises calculating a magnetic characteristic value based on each of the magnetic interaction calculation methods.
The program according to still another aspect of this invention causes, when executed on a computer, the computer to execute each of the magnetic interaction calculation methods.
The program according to still another aspect of this invention causes, when executed on a computer, the computer to execute each of the magnetic characteristic value calculation methods. Each of the magnetic characteristic value calculation methods comprises calculating a magnetic characteristic value based on each of the magnetic interaction calculation methods.
These and other objects, features and advantages of the present invention are specifically set forth in or will become apparent from the following detailed descriptions of the invention when read in conjunction with the accompanying drawings.